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1 0.8 0.6 0.4 0.2 0 10 8 5000 confirmation lag (N) 2 1000 0 0 6 4000 4 3000 2000 trade size (d) Figure 3.3: Trade Size, Confirmation Lag and Probabilistic Finality We now incorporate this basic structure of a cryptocurrency into a general equilibrium framework of a monetary economy. This step is essential, as a cryptocurrency is a closed looped system (see introduction) and the cryptocurrency can only have value if it circulates in the economy. The value of the cryptocurrency will determine the rewards that miners receive. These rewards determine the mining effort and, thus, the incentives to double spend. This in turn will feed back into the value of the currency and its usefulness as a medium of exchange. Our framework can then be used to explore the optimal design of a cryptocurrency and to estimate the actual surplus produced by an existing cryptocurrency such as Bitcoin. 4 General Equilibrium Framework 4.1 Dynamic Model Our model is based on Lagos and Wright (2005).22 Time is discrete and denoted by t = 0, 1, 2, .... There are a large number B of buyers and a large number S = Bσ of sellers, where σ ∈ (0,1). There is also a large number M of miners. While the general setting can also be analyzed, this section focuses on the case of competitive mining (M → ∞) which, as argued in footnote 17, is 22This framework is useful because it allows us to study frictions that necessitate the usage of money while still keeping the distribution of balances analytically tractable. 20 Finality (1-P)PDF Image | The Economics of Cryptocurrencies Bitcoin and Beyond
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